A Jones matrix and a Mueller matrix are generally used to show a characteristic of an optical system of a semiconductor exposure apparatus and the like. A Jones matrix is a matrix with two rows and two columns, and expresses an optical characteristic of an optical element that passes a completely-polarized light.
When a light with a completely-polarized light that may be expressed by a Jones vector passes through an optical element to experience some conversion, a Jones matrix may be used for expressing a characteristic of the optical element.
The Jones matrix is advantageous in that calculation may be done in a conventional optical simulator using an electric-field vector.
However, the Jones matrix can deal with a completely-polarized light only (a light that does not include a non-polarized light component), and cannot handle a partially-polarized light including a non-polarized light component in a general optical simulator. Also, the Jones matrix cannot deal with an optical system having a property of generating a light with a polarized light component, and, on the other hand, dissolving a polarized light component.
A Stokes parameter and a Mueller matrix are generally used to express a characteristic of an optical system having a characteristic of generating an illumination light with a partially-polarized light, generating or dissolving a polarized light component. The Mueller matrix is a matrix with 4 rows and 4 columns for expressing an optical property of an optical element through which a partially-polarized light expressed by a Stokes parameter passes. A Stokes parameter may express: intensity of light as a whole; intensity of 0° linearly-polarized light component; intensity of 45° linearly-polarized light component; and intensity of circular-polarized light component, with parameters. Accordingly, the Stokes parameter may express a partially-polarized light including a non-polarized light component. When a partially-polarized light that may be expressed by a Stokes parameter passes through an optical element, and receives some conversion therefrom, a Mueller matrix may express the characteristic of the optical element.
In recent years, in order to improve a condition of an image of a mask pattern of a semiconductor exposure apparatus, a polarization state of an illumination light is controlled in a positive manner. Therefore, it is requested that a polarization state of an illumination light which passed a mask pattern be measured, for example. The inventor of this application has already proposed a device for measuring a state of polarization of an illumination light.
On the other hand, in a simulation device for calculating a state of an image provided by an optical system, and reproducing the image in a simulative manner, a Jones vector and a Jones matrix are used in view of easiness in operation. Thus, when a Stokes parameter that indicates a measured characteristic of an optical system is input to a simulation device, it is necessary to convert measured Stokes parameter into a Jones vector.
However, a Jones vector could deal with a completely-polarized light, but cannot deal with a partially-polarized light. Accordingly, even if a Stokes parameter expressing a partially-polarized light is obtained, the Stokes parameter cannot be input into a simulation device without any conversion. Thus, conventional technologies cannot provide a correct imaging calculation for an optical system having a characteristic of generating an illumination light with a partially-polarized light, generating or dissolving a polarized light component.